The Analysis of Matter

the proposition, but merely suggested it, and led to our finding the real proof. But, in view of the fact that the distinction between empirical and a priori is epistemological, not logical, it is obviously possible for a proposition to change from the one class to the other, since the classification involves reference to the organization of a particular person's knowledge at a particular time. So regarded, the distinction might seem unimportant; but it suggests some less subjective distinctions, which are what we really wish to consider. Kant's philosophy started from the question: How are synthetic a priori judgments possible? Now we must first of all make a distinction. Kant is concerned with knowledge, not with mere belief. There is no philosophical problem in the fact that a man can have a belief which is synthetic and not based on experience—e.g. that this time the horse on which he has put his money will win. The philosophical problem arises only if there is a class of synthetic a priori beliefs which is always true. Kant considered the propositions of pure mathematics to be of this kind; but in this he was misled by the common opinion of his time, to the effect that geometry, though a branch of pure mathematics, gave information about actual space. Owing to non-Euclidean geometry, particularly as applied in the theory of relativity, we must now distinguish sharply between the geometry applicable to actual space, which is an empirical study forming part of physics, and the[Pg 175] geometry of pure mathematics, which gives no information as to actual space. Consequently this instance of synthetic a priori knowledge, upon which Kant relied, is no longer available. Other kinds have been supposed to exist—for example, ethical knowledge, and the law of causality; but it is not necessary for our purposes to decide whether these kinds really exist or not. So far as physics is concerned, we may assume that all real knowledge is either dependent (at least in part) upon perception, or analytic in the sense in which pure mathematics is analytic. The Kantian synthetic a priori knowledge, whether it exists or not, seems not to be found in physics—unless, indeed, the principle of induction were to count as such. But the principle of induction, as we have already seen, has its origin in physiology, and this suggests a quite different treatment of a priori beliefs from that of Kant. Whether there is a priori knowledge or not, there undoubtedly are, in a certain sense, a priori beliefs. We have reflexes which we intellectualize into beliefs; we blink, and this leads us to the belief that an object touching the eye will hurt it. We may have this belief before we have experience of its truth; if so, it is, in a sense, synthetic a priori knowledge—i.e. it is a belief, not based upon experience, in a true synthetic proposition. Our belief in induction is essentially analogous. But such beliefs, even when true, hardly deserve to be called knowledge, since they are not all true, and therefore all require verification before they ought to be regarded as certain. These beliefs have been useful in generating science, since they supplied hypotheses which were largely true; but they need not survive untested in modern science. I shall therefore assume that, at any rate in every department relevant to physics, all knowledge is either analytic in the sense in which logic and pure mathematics are analytic, or is, at least in part, derived from perception. And all knowledge[Pg 176] which is in any degree necessarily dependent upon perception I shall call "empirical." I shall regard a piece of knowledge as necessarily dependent upon perception when, after a careful analysis of our grounds for believing it, it is found that among these grounds there is the cognition of an event in time, arising at the same time as the event or very shortly after it, and fulfilling certain further criteria which are necessary in order to distinguish perception from certain kinds of error. These criteria will occupy us in the next chapter. In a science, there are two kinds of empirical propositions. There are those concerned with particular matters of fact, and those concerned with laws induced from matters of fact. The appearances presented by the sun and moon and planets on certain occasions when they have been seen are particular matters of fact. The inference that the sun and moon and planets exist even when no one is observing them—in particular, that the sun exists at night and the planets by day—is an empirical induction. Heraclitus thought the sun was new every day, and there was no logical impossibility in this hypothesis. Thus empirical laws not only depend upon particular matters of fact, but are inferred from these by a process which falls short of logical demonstration. They differ from propositions of pure mathematics both through the nature of their premisses and through the method by which they are inferred from these premisses. In an advanced science such as physics, the part played by pure mathematics consists in connecting various empirical generalizations with each other, so that the more general laws which replace them are based upon a larger number of matters of fact. The passage from Kepler's laws to the law of gravitation is the stock instance. Each of the three laws was based upon a certain set of facts; all three sets of facts together formed the basis of the law of gravitation. And, as usually[Pg 177] happens in such cases, new facts, not belonging to any of the three previous sets, were found to support the new law—for instance, the facts of tides, of lunar motion, and of perturbations. Epistemologically, in such cases, a fact is a premiss for a law; logically, most of the relevant facts are consequences of the law—i.e. all except those required to determine the constants of integration. In history and geography, the empirical facts are, at present, more important than any generalizations based upon them. In theoretical physics, the opposite is the case: the fact that the sun and moon exist is chiefly interesting as affording evidence of the law of gravitation and the laws of the transmission of light. In a philosophic analysis of physics, we need not consider particular facts except when they form the evidence for a theory. It is of course part of the business of such an analysis to consider what all particular facts have in common, and how they come to be known; but such inquiries are general. We are interested in the concept of topography, but not in the actual topography of the universe; at least, we are not interested in it for its own sake, but only as affording the evidence for general laws. We have, in view of the above considerations, several different matters to consider, before we can return to actual physics. We have first to consider the nature and validity of the process we have called "perception"; next we have to investigate the general character of the facts known by perception; and lastly we have to examine the inference from facts of perception to empirical laws. After disposing of these topics, we shall resume contact with physics, asking ourselves now, not what physics asserts, but what justification it has for its assertions, and what inessential modifications will increase this justification. FOOTNOTES: [41] I do not wish to prejudice the question whether there is such a process as "introspection," but only to include it if it exists. [Pg 178] CHAPTER XVIII OUR KNOWLEDGE OF PARTICULAR MATTERS OF FACT IN this chapter, I wish to consider whatever would ordinarily pass for knowledge of particular matters of fact, in so far as this is not obtained by a process of deliberate scientific inference. I want to consider this as far as possible independently of the scientific laws based upon it, though not completely without reference to the primitive beliefs by which common sense draws inferences from perceptions. In particular, I wish to abstain from introducing the causal theory of perception, unless, on investigation, this should prove impossible. It will be understood that my purpose is epistemological: I am considering perception because it is involved in the premisses of empirical sciences, not because it is interesting as a mental process. It is of course necessary to consider its intrinsic character, but we do not do this for its own sake, we do it for the sake of the light that it may throw upon the character and extent of our knowledge. [Pg 179] We are met at the outset by a difficulty due to the fact that philosophical terminology is inappropriate when the views to be expressed are in any way unusual. "Knowledge" and "belief" both have connotations which are inconvenient for the purpose I have in view. They are both commonly applied in orthodox psychology to something conscious and explicit, such as is, or may be, already expressed in words. For our purposes, it is desirable to include more primitive occurrences, such as may be supposed to exist in animals. Obviously a bird can see an approaching man, and fly away in consequence. I wish to include under "perception" what happens in the bird, and also to say that the bird "knows" something when it sees a man, though I shall not venture to say what it knows. But at this point a good deal of caution is necessary. My knowledge of the bird is part of my knowledge of the external world, and is partly, if not wholly, physical knowledge. Therefore when I am asking: how do I know about the physical world? I have no right to begin by comparing my knowledge with that of a bird. I must start from myself and my own cognitions, and use the bird only to suggest hypotheses. This caution applies also to what was said in Chapter XV. Again, there is always a danger, in epistemology, of putting the less certain before the more certain. My knowledge of the process of perceiving is less certain, and less primitive, than my knowledge of percepts. When I say, "I know that I have just heard a clap of thunder," I am saying something not so indubitable as when I say, "There has just been a clap of thunder." It is facts of this latter kind that are required as premisses in physics. A man might be completely competent as a physicist if he knew such propositions as "There has just been a clap of thunder" even if he knew no propositions such as "I know that there has just been a clap of thunder." The consideration of our knowing, as opposed to what we know, is forced on us by the fact that what we think we know sometimes turns out to be false; if this were not the case, an analysis of matter need not consider our knowing at all. As it is the case, we are compelled to examine our knowing, as well as what we know, with a view to discovering, if possible, how to minimize the risk involved in taking as knowledge what, on reflection, we still believe to be knowledge. We are often urged to adopt an artificial naivete in investigating problems concerning what we know; if we do not do so, we are accused of the "psychologist's fallacy." Now in certain problems this caution is quite proper, but in others it is not. My problem is: What do I, here and now, know about the external world, and how do I know it? It is obvious that my knowledge of the external world cannot be dependent[Pg 180] upon (say) how long it takes a fish to learn to recognize the man who feeds it, since this supposes that I know all about the fish and the man and the feeding. Facts about the perceptions of babies, such as we considered in Chapter XV., come